Answer:
2x²+1/4πx², and 122,850 sq. ft.
Step-by-step explanation:
We know that the short side of the rectangle is x. The long side is 2 times longer than the short side; this means the long side is 2x. This makes the area of the rectangular portion of the stadium
x(2x) = 2x².
We have two semi-circles at each end. The diameter of each semi-circle is x; this makes the radius 1/2x.
The area of a circle is A = πr²; since these are semi-circles, the area would be given by A = 1/2πr². Using 1/2x in place of r, we have
A = 1/2π(1/2x)² = 1/2π(1/4x²) = 1/8πx²
Using 22/7 for π, we have
A = 1/8(22/7)x² = 22/56x²
Since there are 2 semi-circles, this gives us
2(22/56x²) = 44/56x²
Simplifying this, we have
A = 22/28x² = 11/14x²
This gives us the expression
2x²+11/14x² for our expression for the area.
(Without using 22/7 for pi, we have
2x²+2(1/8πx²) = 2x²+2/8πx² = 2x²+1/4πx²
Using 210 for x and 22/7 for π, we have
A = 2(210²)+1/4(22/7)(210²) = 88200+34650= 122,850
